Package 'fpoValue'

Scale economies from aggregation

Description

Estimates the gross savings an FPO can generate by aggregating members' produce and purchases, from three sources:

Transport consolidation

Without the FPO, each member carries produce to the market in small vehicles. With the FPO, members carry produce to a nearby collection centre and the FPO moves the pooled volume in large vehicles. Trip-based costs make the per-unit cost of both legs depend on the quantity carried.

Bulk input procurement

A tiered discount schedule is applied to each member's own input purchase and to the pooled purchase.

Grading

Selling sorted grades instead of an ungraded lot earns a price premium per unit equal to the grade-weighted price minus the ungraded price, less any grading cost.

Savings are reported in total, per unit and per member. Transport savings are member-specific; the bulk leg is allocated in proportion to quantity, as are grading premiums. These are *potential* savings: whether members receive them depends on the FPO's pricing and dividend policy, which [member_benefit()] evaluates.

Usage

aggregation_savings(
  quantity,
  distance_market,
  distance_centre = 0,
  centre_to_market = NULL,
  small_capacity = 1,
  small_cost_per_km = 0,
  small_fixed_trip = 0,
  bulk_capacity = 10,
  bulk_cost_per_km = 0,
  bulk_fixed_trip = 0,
  input_quantity = 0,
  input_price = 0,
  discount_tiers = NULL,
  grade_shares = NULL,
  grade_prices = NULL,
  ungraded_price = NULL,
  grading_cost = 0
)

Arguments

quantity	Quantity marketed by each member.
distance_market	One-way distance (km) from each farm to the market.
distance_centre	One-way distance (km) from each farm to the collection centre.
centre_to_market	One-way distance (km) from the collection centre to the market.
small_capacity, small_cost_per_km, small_fixed_trip	Capacity, cost per km and fixed cost per trip of the small vehicles used by members.
bulk_capacity, bulk_cost_per_km, bulk_fixed_trip	Capacity, cost per km and fixed cost per trip of the FPO's bulk vehicles.
input_quantity	Quantity of inputs bought by each member.
input_price	Undiscounted input price per unit.
discount_tiers	Optional data frame with columns 'min_quantity' and 'discount' (share off 'input_price') defining a bulk discount schedule.
grade_shares, grade_prices	Optional vectors giving the share of produce in each grade and the price of each grade.
ungraded_price	Price of an ungraded lot.
grading_cost	Cost of grading per unit.

Value

A list of class 'aggregation_savings' with 'by_source' (total and per-unit savings for transport, inputs and grading), 'by_member' (savings per member) and 'total'.

Examples

q <- c(4, 8, 15, 25, 60)
aggregation_savings(q, distance_market = 30, distance_centre = 3,
                    centre_to_market = 30, small_capacity = 5,
                    small_cost_per_km = 20, bulk_capacity = 100,
                    bulk_cost_per_km = 45,
                    input_quantity = c(2, 3, 5, 8, 20), input_price = 1300,
                    discount_tiers = data.frame(min_quantity = c(10, 30),
                                                discount = c(0.03, 0.06)),
                    grade_shares = c(0.5, 0.3, 0.2),
                    grade_prices = c(2000, 1600, 1100),
                    ungraded_price = 1550, grading_cost = 30)

---

Break-even throughput, membership and procurement price

Description

Finds the volume an FPO must handle to cover its fixed costs (and an optional surplus target) given the per-unit margin between its sale price and the price it pays members:

$Q^{*} = \frac{F + T - M_{inputs}}{p^{sale} - p^{m} - h},$

where $F$ is fixed cost, $T$ the surplus target and $M_{inputs}$ the margin from the input business. It also reports the number of members needed at the average member volume, the margin of safety at the current volume, and the highest member price the FPO can pay at the current volume while breaking even, which bounds how much of the aggregation gain can be passed to farmers through prices.

Usage

break_even_volume(
  fixed_cost,
  sale_price,
  member_price,
  handling_cost = 0,
  input_margin = 0,
  target_surplus = 0,
  avg_member_volume = NULL,
  current_volume = NULL
)

Arguments

fixed_cost	FPO fixed operating cost for the period.
sale_price	Price the FPO realises per unit.
member_price	Price the FPO pays members per unit.
handling_cost	FPO handling cost per unit.
input_margin	Surplus from the input business for the period.
target_surplus	Surplus the FPO aims to retain (for reserves or dividends).
avg_member_volume	Optional average volume per member.
current_volume	Optional current throughput.

Details

All arguments are vectorised and recycled, so a grid of scenarios can be evaluated in one call.

Value

A data frame of class 'break_even_volume' with the inputs and 'unit_margin', 'break_even_volume', 'members_needed', 'margin_of_safety' (share by which current volume exceeds break-even) and 'max_member_price' (at the current volume). Break-even volume is 'Inf' when the unit margin is not positive and the costs are not already covered.

Examples

break_even_volume(fixed_cost = 6e5, sale_price = 1650,
                  member_price = c(1450, 1500, 1550),
                  handling_cost = 60, input_margin = 1e5,
                  avg_member_volume = 15, current_volume = 6000)

---

Compare individual and collective marketing scenarios

Description

Evaluates the same set of members under alternative marketing channels, for example individual sale to a village trader, individual sale in a wholesale market, FPO aggregation, FPO aggregation with grading, and an FPO contract with a processor or retailer. Each scenario is described by one row of 'scenarios':

scenario

Name.

member_price

Price received by members.

member_cost

Members' transaction cost per unit.

sale_price

Price realised by the FPO; 'NA' for individual channels.

handling_cost, fixed_cost, dividend_share

Optional FPO parameters (default 0).

Member net return is $q_i(p^m - c^m) + D_i$. For FPO channels the FPO surplus and patronage dividends are computed as in [member_benefit()]. Each scenario is compared with the 'baseline' scenario: the gain in members' net returns, the FPO's retained surplus, the total value created relative to the baseline, the member share of that value, the share of members better off, and the gain received by the smallest half of suppliers.

Usage

collective_marketing_scenarios(
  quantity,
  scenarios,
  baseline = NULL,
  group = NULL
)

Arguments

quantity	Quantity marketed by each member.
scenarios	Data frame of scenarios (see Details).
baseline	Name of the baseline scenario; defaults to the first row.
group	Optional group of each member for group-wise gains.

Value

A list of class 'collective_marketing_scenarios' with 'summary' (one row per scenario), 'member_returns' (matrix of member net returns, members by scenarios) and, if 'group' is given, 'group_gain' (gain per member by group and scenario). A 'plot()' method compares member gains and retained surplus across scenarios.

Examples

q <- c(5, 8, 12, 20, 35, 60)
sc <- data.frame(
  scenario = c("village trader", "mandi", "FPO pooled", "FPO graded"),
  member_price = c(1300, 1450, 1480, 1540),
  member_cost = c(10, 140, 40, 55),
  sale_price = c(NA, NA, 1650, 1760),
  handling_cost = c(0, 0, 60, 90),
  fixed_cost = c(0, 0, 8000, 12000),
  dividend_share = c(0, 0, 0.5, 0.5))
res <- collective_marketing_scenarios(q, sc,
         group = c("marginal", "marginal", "small", "small",
                   "medium", "large"))
res
plot(res)

---

Member-level distributional accounting of FPO benefits

Description

Separates the total surplus generated by a farmer producer organisation (FPO) from the benefits actually received by member farmers.

Usage

member_benefit(
  quantity,
  outside_price,
  member_price,
  sale_price,
  outside_cost = 0,
  member_cost = 0,
  handling_cost = 0,
  fixed_cost = 0,
  input_quantity = 0,
  input_market_price = 0,
  input_member_price = 0,
  input_bulk_price = 0,
  dividend_share = 0,
  dividend_rule = c("patronage", "equity", "equal"),
  equity = NULL,
  group = NULL,
  member_id = NULL
)

Arguments

quantity	Quantity each member sells through the FPO.
outside_price	Price each member would receive outside the FPO.
member_price	Price the FPO pays each member.
sale_price	Price the FPO realises when selling the pooled produce.
outside_cost	Member transaction cost per unit outside the FPO.
member_cost	Member transaction cost per unit when delivering to the FPO.
handling_cost	FPO handling, grading and transport cost per unit.
fixed_cost	FPO fixed operating cost for the period (staff, rent, compliance, depreciation).
input_quantity	Quantity of inputs each member buys through the FPO.
input_market_price	Price of inputs in the open market.
input_member_price	Price the FPO charges members for inputs.
input_bulk_price	Price the FPO pays for inputs in bulk.
dividend_share	Share of positive FPO surplus paid out as dividends (0 to 1).
dividend_rule	How dividends are allocated: '"patronage"' (in proportion to quantity), '"equity"' (in proportion to 'equity') or '"equal"' (equal per member).
equity	Share capital held by each member; required for 'dividend_rule = "equity"'.
group	Optional farm-size or social group of each member.
member_id	Optional member identifiers.

Details

**FPO account.** The FPO buys members' produce at 'member_price', sells it at 'sale_price', incurs handling costs per unit and fixed operating costs, and may run an input business buying at 'input_bulk_price' and selling to members at 'input_member_price'. Its net surplus is

$S = \sum_i q_i (p^{sale} - p^{m}_i - h) + \sum_i x_i (w^{m} - w^{bulk}) - F.$

A share 'dividend_share' of positive surplus is distributed as dividends; the rest is retained.

**Member account.** Relative to the member's outside option (selling individually at 'outside_price' with transaction cost 'outside_cost' and buying inputs at 'input_market_price'), member $i$ gains

$B_i = q_i (p^m_i - p^{out}_i) + q_i (c^{out}_i - c^m_i) + x_i (w^{mkt} - w^{m}) + D_i.$

**Value created** is $\sum_i (B_i - D_i) + S$, which equals $\sum_i B_i$ plus retained surplus. The member share of value created shows how much of the FPO's economic contribution actually reaches farmers. Distribution across members is summarised by the Gini coefficient of benefits (when all benefits are non-negative), the concentration index of benefits ranked by quantity marketed (positive values mean benefits are concentrated among larger suppliers), the benefit share of the smallest half of suppliers compared with their quantity share, the share of members made worse off, and, if 'group' is given, benefit shares and benefit per member by group (for example marginal, small, medium and large farmers).

Per-member arguments accept a scalar or one value per member. Per-unit transaction costs can be taken from [transaction_costs()].

Value

A list of class 'member_benefit' with

members

Data frame of benefit components per member: 'price_gain', 'cost_saving', 'input_saving', 'dividend' and 'total'.

fpo

Named vector: output margin, input margin, fixed cost, net surplus, dividends paid and retained surplus.

value

Named vector: value created, total member benefit, retained surplus, member share of value created, member benefit per unit marketed.

distribution

List with 'metrics' and 'by_group'.

Examples

q <- c(5, 8, 12, 20, 35, 60)
size <- c("marginal", "marginal", "small", "small", "medium", "large")
mb <- member_benefit(q, outside_price = 1400, member_price = 1480,
                     sale_price = 1650, outside_cost = 140,
                     member_cost = 40, handling_cost = 60,
                     fixed_cost = 8000, input_quantity = q / 5,
                     input_market_price = 1350, input_member_price = 1300,
                     input_bulk_price = 1250, dividend_share = 0.5,
                     group = size)
mb
mb$distribution$by_group

---

Plot collective marketing scenarios

Description

Stacked bars of the gain in member net returns and the FPO's retained surplus, relative to the baseline, for each scenario.

Usage

## S3 method for class 'collective_marketing_scenarios'
plot(x, ...)

Arguments

x	A [collective_marketing_scenarios()] object.
...	Further arguments passed to [graphics::barplot()].

Value

'x', invisibly.

Examples

sc <- data.frame(scenario = c("individual", "FPO"),
                 member_price = c(1400, 1480), member_cost = c(120, 40),
                 sale_price = c(NA, 1650), handling_cost = c(0, 60),
                 fixed_cost = c(0, 5000), dividend_share = c(0, 0.5))
plot(collective_marketing_scenarios(c(5, 10, 20, 40), sc))

---

Transaction costs of a marketing channel

Description

Computes, for each farmer, the full cost of selling through one marketing channel. Transport is trip-based, so costs per unit fall with the quantity carried per trip:

$transport_i = trips_i \times (2\,d_i\,c_{km} + c_{trip}),\quad trips_i = \lceil q_i / capacity \rceil.$

Other components are commission (a share of sale value), market fees and handling charges per unit, the opportunity cost of the farmer's time per trip, the value of produce rejected or unsold, and the interest cost of delayed payment.

Usage

transaction_costs(
  quantity,
  price,
  distance,
  vehicle_capacity = 1,
  cost_per_km = 0,
  fixed_per_trip = 0,
  commission = 0,
  market_fee = 0,
  handling = 0,
  time_hours = 0,
  wage = 0,
  rejection = 0,
  payment_delay = 0,
  interest_rate = 0.12,
  label = NULL
)

Arguments

quantity	Quantity sold by each farmer.
price	Sale price per unit (scalar or one per farmer).
distance	One-way distance (km) from farm to point of sale.
vehicle_capacity	Quantity carried per trip.
cost_per_km	Vehicle cost per km.
fixed_per_trip	Fixed cost per trip (loading, tolls, hire minimum).
commission	Commission as a share of sale value.
market_fee	Market fee or levy per unit.
handling	Handling, packing and loading cost per unit.
time_hours	Farmer time per trip (travel, waiting, bargaining).
wage	Opportunity cost of farmer time per hour.
rejection	Share of quantity rejected or sold at zero value.
payment_delay	Days between sale and payment.
interest_rate	Annual interest rate used to value payment delay.
label	Optional channel name stored with the result.

Details

Call the function once for each channel (for example individual sale in a wholesale market and delivery to an FPO collection centre) and pass the resulting 'per_unit' costs to [member_benefit()] or [collective_marketing_scenarios()].

Value

A data frame of class 'transaction_costs' with one row per farmer: 'quantity', 'trips', 'transport', 'commission', 'fees', 'handling', 'time_cost', 'rejection_cost', 'delay_cost', 'total', 'per_unit' and 'share_of_value'.

Examples

q <- c(5, 12, 30, 80)
mandi <- transaction_costs(q, price = 1500, distance = 35,
                           vehicle_capacity = 10, cost_per_km = 25,
                           commission = 0.06, market_fee = 15,
                           time_hours = 8, wage = 50,
                           payment_delay = 7, label = "mandi")
centre <- transaction_costs(q, price = 1500, distance = 4,
                            vehicle_capacity = 10, cost_per_km = 25,
                            time_hours = 1.5, wage = 50,
                            payment_delay = 10, label = "FPO centre")
data.frame(quantity = q, mandi = mandi$per_unit,
           centre = centre$per_unit)

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